Is relativistic mass an illusion

If relativistic mass is only seen by an observer outside of the particular frame in question, it must be an illusion. You could have several inertial frames moving about at different speeds and no one could agree on the relativistic mass of each one, yet they would all agree that their own mass is at rest.

It makes it sound like gamma is some kind of resistance in space despite the fact that a continuous 1G acceleration will cover more distance at a faster and faster rate according to your clocks on the ship. Earth time is the one that seems to be stuck at the speed of light. That could be a relevant factor on a trip.

It is no more an illusion than the kinetic energy of that mass (which is in fact what the extra mass could be called). Take the difference between the relativistic mass and the rest mass, and you get the kinetic energy. Of course kinetic energy depends on how fast you consider the object to be moving.

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Our voting system is broken! It nearly guarantees that we will have only two political parties that have any chance of winning, and that they will be very similar.

I disagree. That view pretty much wipes out almost all useful physics. How much useful physics can you do without some observer-dependent quantities?

The problem with relativistic mass is not that it is illusory. Velocity and energy are equally frame-dependent but are quite useful and very non-illusory concepts. The chief problem with relativistic mass is that it is synonymous with energy (literally synonymous; m=E/c2). The concept of relativistic mass doesn't add much of value (just use energy) but it certainly does add confusion.

DH, I assure you that the modern point of view is exactly what I have said.

A physical system will come with some automorphisms. The only "meaningful" observables are those that are invariant under these automorphisms. If lets say observable A can be transformed into observable B via an automorphism then how can we attach a real physical meaning to A (or indeed B).

That is not to say that A is not useful in some situations, but it cannot have some deeper meaning. The example of relativistic mass springs to mind here. It may be useful for some things, but as we have seen it is not an "absolute" and the frames need to be specified. (This is reminiscent of gauge fixing).

For the case of special relativity this is the Poincare group.

For gauge theories this is the relevant gauge group (and if relativistic the Poincare group also)

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"In physics you don't have to go around making trouble for yourself - nature does it for you" Frank Wilczek.

I have a question on my mind for some time and I would be grateful if someone could help me figure out the answer. So, let's consider an imaginary experiment: two mirrors in space, far away from any gravitational effect, parallel to each other, and 2 beams of light falling at a small incidental angle on one of the mirrors, such that the beams travel reciprocal parallel great distances. The question is would they attract to each-other, and get closer together? From the mirrors’ frame, the classical gravitational law would predict that they do, due to their mass m=hυ/c^2…

I have a struggle to understand how relativistic mass is real if the observer that is traveling close to the speed of light sees the rest of the universe as massive and time dilated but the at rest observer sees only the speeding object as time dilated and massive. How can both be correct? also when the fast observer is slowed down only his time dilation proves to be real, the rest of the universe has aged at the same rate it always has. Only the time dilation of the fast observer is real when he slows down.

SR has three relationships, one for time, distance and mass. The relativistic mass is important because it allows us to do an energy balance and therefore differentiate between relative references. The M is connected to E=MC2 with E connected to kinetic energy.

Try this thought experiment. We start with three stationary references separated a distance d in a triangle. We label one and give it velocity V. From the point of view of either stationary reference, we see one stationary and one reference with velocity. From the point of view of the moving reference, we see two stationary references appearing to move. One can see the energy balance is different, so relative can cause problems in terms of energy conservation. With two references, it is harder to do an energy balance, so we have 50/50 odds of picking the correct reference that is moving because of energy (has the relativistic mass).

This goes back to your question, is relativistic mass real or just a mathematical concept? If it was real, we should be able to measure it and differentiate relative reference. If it is just a concept, we are stuck at 50/50 odds of getting it right with respect to energy balance reality. We could pick what is convenient for us, and then have 50/50 odds. We can still learn things but we might assume to much or to little energy. This will have an impact on subsequent assumptions.

It may be important to figure out how to measure relativistic mass, from a distance, to confirm if we have the energy balance correct. If we go back to our three reference scenario, if we could measure relativistic mass, the moving reference would see V but no m. The stationary would both see V and m. Based on that both know who is stationary and moving, even if there are special effects in t, d.

I have a struggle to understand how relativistic mass is real if the observer that is traveling close to the speed of light sees the rest of the universe as massive and time dilated but the at rest observer sees only the speeding object as time dilated and massive. How can both be correct?

"How can both be correct" isn't a meaningful question unless you give some apparent reason why they can't.

also when the fast observer is slowed down only his time dilation proves to be real, the rest of the universe has aged at the same rate it always has. Only the time dilation of the fast observer is real when he slows down.

SR has three relationships, one for time, distance and mass. The relativistic mass is important because it allows us to do an energy balance and therefore differentiate between relative references. The M is connected to E=MC2 with E connected to kinetic energy.

Or you could have an invariant mass, and then the kinetic energy is the frame-dependent term. Relativistic mass is by no means required, and screws up the representation of the momentum 4-vector.